Consider a two-server, ordered entry, queuing system with heterogeneous servers and finite waiting rooms in front of the servers. Service times are negative exponentially distributed. The arrival process is deterministic. A matrix solution for the steady state probabilities of the number of customers in the system is derived. The overflow probability will be used to formulate the stability condition of a closed-loop conveyor system with two work stations.
Nawijn, W. M. (1984). On a two-server finite queuing system with ordered entry and deterministic arrivals. European journal of operational research, 18(3), 388-395. https://doi.org/10.1016/0377-2217(84)90161-9